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Re: Why am I getting this error?

• To: mathgroup at smc.vnet.net
• Subject: [mg60352] Re: Why am I getting this error?
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Wed, 14 Sep 2005 03:27:19 -0400 (EDT)
• Organization: The University of Western Australia
• References: <dg69s7$a9j$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

In article <dg69s7$a9j$1 at smc.vnet.net>, ksmath <kdsimon at uiuc.edu> 
wrote:

> I am attempting to solve a system with 3 pde's and I keep getting this error 
> even though I think all of my equations have independent variables:
> 
> NDSolve::dvnoarg: The function v appears with no arguments.
> 
> If anyone could find the mistake in my code I would really appreciate it.  
> C,V, and R are the dependent variables, and t (time) and x(distance-does not 
> depend on time) are the independent variables.  All other variables are 
> constants.

Some comments:

[1] Although your equations are impossible to read due to some 
mysterious symbols, the equation involving r appears to be completely 
decoupled from the equations involving c and v -- so solve this one 
first.

[2] You are using the symbols r and v as subscripts as well as using 
them as the names of functions in the pde's. This could cause problems 
(unless you "symbolize" such subscripted symbols using the Notation 
package).

[3] To use NDSolve, all parameters must resolve to numerical values. 
There are a number of parameters in your equations for which no 
numerical values are defined or implied.

[4] In the NDSolve command, you are solving for functions q1 and q2 -- 
these are not defined.

Since you are at UIUC, I suggest that you attend the upcoming Wolfram 
Research TechConf <http://www.wolfram.com/news/events/techconf2005/>. 
There will be a number of helpful sessions on solving differential 
equations using Mathematica. In addition, at the Training tab, you will 
see there are several Wolfram Education Group sessions that are likely 
to be of interest.

Cheers,
Paul

> Thank you for any assistance you can provide me.
> 
> \!\(\(rRHS\  = \ \(d\_r\) D[r[t, 
>       x], {x, 2}] + β \((1 - \((r[t, x] - r\_base)\)/\((k\_r - 
>         r\_base)\))\) \((r[t, x] - r\_base)\);\)\[IndentingNewLine]
>   \(vRHS\  = \ \(d\_v\) D[v[t, x], {x, 2}] - Ï?\ v[t, x]\  - 
>             η\ v[t, x]\ c[t, x]/\((γ\_1 + v[t, x])\) + If[
>     q\_large < q\_min, λ \((q\_large - q\_min)\), 0];\)\[IndentingNewLine]
>   \(\(cRHS\  = \ D[c[t, x]\ v[t, x]\ D[v[t, x], x], x] + If[v[
>         t, x] â?¥ v\_g, Ï?\ v[t, x]\ c[t, 
>         x]\ /\((γ\_2 + 
>             v[t, x])\), Ï? \((v[t, x] - 
>               v\_d)\) c[t, x]];\)\(\[IndentingNewLine]\)
>   \)\[IndentingNewLine]
>   \(reqn\  = D[r[t, x], t]\  == \ rRHS;\)\[IndentingNewLine]
>   \(veqn\  = \ D[v[t, x], t]\  == \ vRHS;\)\[IndentingNewLine]
>   \(ceqn\  = \ D[c[t, x], t]\  == \ cRHS;\)\)
> 
> BC1 = Derivative[0, 1][r][t, 0] == 0;
> BC2 = Derivative[0, 1][r][t, 1] == 0;
> BC3 = Derivative[0, 1][v][t, 0] == 0;
> BC4 = Derivative[0, 1][v][t, 1] == 0;
> BC5 = c[t, 0] == 1;
> BC6 = c[t, 1] v[t, 1] Derivative[0, 1][v][t, 1] == 0;
> 
> \!\(\(c\_init = \(c\_o\) Exp \((\(-150\) x\^2)\) == c[0, 
>           x];\)\[IndentingNewLine]
>   \(r\_init = \((K\_r - 
>           r\_base)\) Exp \((\(-100\) x\^2)\) + r\_base == r[0, x];\)\
> \[IndentingNewLine]
>   \(v\_init = \((v\_g - v\_d)\)/\((2  v\_o)\) == v[0, x];\)\)
> 
> \!\(\(solution\  = \ NDSolve[{reqn, \ veqn, \ ceqn, q1\_i,
>          q2\_i, \ c\_init, \ v\_init, \ 
>           r\_init, \ BC1, \ BC2, \ BC3, \ BC4, \ BC5, \ BC6}, {r[t, x], v[t, 
>           x], c[t, x], q1[t, x], q2[t, x]}, {t, 0, 1}, {x, 0, 1}];\)\)
> 
> Any help is much appreciated.
> 
> Katie

_______________________________________________________________________
Paul Abbott                                      Phone:  61 8 6488 2734
School of Physics, M013                            Fax: +61 8 6488 1014
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